Question: Simplify the following expression and state the condition under which the simplification is valid: $t = \dfrac{a^2 - 4a - 60}{a^2 - 2a - 48}$
Explanation: First factor the expressions in the numerator and denominator. $ \dfrac{a^2 - 4a - 60}{a^2 - 2a - 48} = \dfrac{(a - 10)(a + 6)}{(a - 8)(a + 6)} $ Notice that the term $(a + 6)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(a + 6)$ gives: $t = \dfrac{a - 10}{a - 8}$ Since we divided by $(a + 6)$, $a \neq -6$. $t = \dfrac{a - 10}{a - 8}; \space a \neq -6$